Phase-field simulation of microstructure evolution coupled to plastic deformation: Application to Ni-base superalloys and low carbon steel
J. V. Görler.
PhD Thesis, Ruhr-Universität Bochum (2018)
The phase-field method has emerged as the best microstructure evolution simulation method available. Its strength comes among other factors from the ability to include different physical effects and capture the interplay between them. Most importantly thermodynamics, diffusion and mechanics can thus interact on a microstructure level. This work is dedicated to the mechanical modeling, in particular modeling of plastic deformation and its interplay with the microstructure. Plasticity models are embedded in a mechanical framework consisting of a spectral elasticity solver, an elastic homogenization scheme, a large deformation framework and a damage model. Three plasticity models have been adapted to the phase-field method and tested on creep in Ni-base superalloys, the phenomenological crystal plasticity model has been applied in a virtual tensile test of tempered martensite as well. During creep deformation in Ni-base superalloys the $\gamma/\gamma'$ microstructure undergoes a transformation known as rafting. $\gamma'$ precipitates coalesce perpendicular to the loading direction, forming raft shaped structures. This transition is influenced by a delicate balance between elastic repulsion of $\gamma'$ precipitates, anti-phase domain repulsion and removal of misfit by plastic deformation. A model that accounts for these influences has been developed. Plastic strain evolution is simulated by the aforementioned three different plasticity models and the results are compared. The best fit is achieved by the phenomenological crystal plasticity model, the power-law creep model and lacks a hardening formulation and thus can not fit the primary creep stage. For the same reason the dislocation density crystal plasticity model does not achieve the best fit. Creep in Ni-base superalloys is the ideal application for investigating the interplay between microstructure evolution and plasticity, because the rafting of the $\gamma/\gamma'$ microstructure and creep deformation are strongly interconnected. A high rafting rate should in turn lead to an increase in plastic strain rate and vice versa. This has been tested with power-law creep and phenomenological crystal plasticity. While the latter shows the expected result, the former displays the opposite trend. The reason for this can be seen on the microstructure level, where the crystallography information in the crystal plasticity model enables it to interact with the changing microstructure and thus achieves the correct result. Coupling microstructure information and mechanics thus enables the local phenomenological crystal plasticity model to display non-local effects in the simulation of superalloy creep thanks to the microstructure information available. Tempered martensite is the second model system for investigating interaction of microstructure and plasticity. A virtual tensile test under has been performed on samples with three different initial compositions and two different tempering treatments. The tensile test is the last step of a three step simulation procedure of quenching, tempering and tensile testing. The microstructure and composition information of the previous simulations have been carried through. This information is used to locally adjust crystal plasticity and damage parameters. Thus, the process history influences the local and the overall results. Different tempering treatments with the same initial composition yield different stress and strain data. The resulting homogenized stress strain data fits the experimental data well. Additionally to that the simulations provide information on the microstructure level that is not obtainable by experiment, such as damage, stress and plastic strain distribution. By using plasticity models in the multi phase-field framework, complex cross-coupled simulations that can resolve complex interactions are possible. This has been shown for Ni-base superalloys and tempered martensite, where the influence of process history, microstructure evolution kinetics as well as local phase and concentration distribution has been considered and the simulation results have been evaluated with experimental results.